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To estimate the key transmission parameters associated with an outbreak of pandemic influenza in an institutional setting (New Zealand 1918).

Historical morbidity and mortality data were obtained from the report of the medical officer for a large military camp. A susceptible-exposed-infectious-recovered epidemiological model was solved numerically to find a range of best-fit estimates for key epidemic parameters and an incidence curve. Mortality data were subsequently modelled by performing a convolution of incidence distribution with a best-fit incidence-mortality lag distribution.

Basic reproduction number (_{0}) values for three possible scenarios ranged between 1.3, and 3.1, and corresponding average latent period and infectious period estimates ranged between 0.7 and 1.3 days, and 0.2 and 0.3 days respectively. The mean and median best-estimate incidence-mortality lag periods were 6.9 and 6.6 days respectively. This delay is consistent with secondary bacterial pneumonia being a relatively important cause of death in this predominantly young male population.

These _{0 }estimates are broadly consistent with others made for the 1918 influenza pandemic and are not particularly large relative to some other infectious diseases. This finding suggests that if a novel influenza strain of similar virulence emerged then it could potentially be controlled through the prompt use of major public health measures.

The 1918 influenza pandemic reached New Zealand with an initial wave between July and October [

The population of the Featherston Military Camp was that of a large regional town, comprising approximately 8000 military personnel of whom 3220 were hospitalised [

A susceptible-exposed-infectious-recovered (SEIR) model for infectious diseases can be applied to a hypothetical isolated population, to investigate local infection dynamics [

where _{0}) for the particular virus strain causing the outbreak. (The basic reproduction number represents the number of secondary cases generated by a primary case in a completely susceptible population). _{0 }and the average latent period (_{E}), and average infectious period (_{I}), can be calculated using the following relationships:

Other factors that are likely to affect the observed incidence of disease in a pandemic include the following: (i) the initial proportion of population that is susceptible (_{is}); (ii) the proportion of infected cases who develop symptoms (_{ids}); (iii) the infectivity of asymptomatic people relative to the infectivity of symptomatic people (_{as}); and (iv) the proportion of symptomatic cases who present (_{sp}).

In this study, the factors listed above were incorporated into an SEIR model to generate incidence and subsequent mortality models for the influenza pandemic that swept through this military camp. These specific models and the resulting estimates of _{0 }and _{E }and _{I }are described below.

When the SEIR model was applied in this study, assumptions about additional factors that might influence the observed incidence were made. The parameters associated with these assumptions are summarised for 3 possible scenarios (Table _{0 }at the lower, mid-range and higher ends of a likely spectrum, respectively.

Parameters used in the SEIR incidence model*.

Initial proportion of the population susceptible (_{is}) | 1.0 | 0.9 | 0.8 |

Proportion of infected cases who develop symptoms (_{ids}) | 0.95 | 0.81 | 0.67 |

Infectivity of asymptomatic/infectivity of symptomatic people (_{as}) | 0.6 | 0.5 | 0.4 |

Proportion of symptomatic cases who present and are diagnosed as infected with influenza (_{sp}) | 0.95 | 0.88 | 0.8 |

*Based on plausible ranges for pandemic influenza with Scenario 1 being closer to a worse case for impact on health and Scenario 3 being less severe. For example, Scenario 3 assumes 20% of the population may have had immunity from previous influenza pandemics that may have reached New Zealand in the late 19^{th }century – as suggested by Rice [2] and supported by the unusually low mortality rates in the older age groups for this pandemic in New Zealand [2].

Equations 1 and 2 were modified to take the above parameters into account, as follows:

Equations 3, 4, 8 and 9 are a system of non-linear differential equations, amenable to solution by the Runge-Kutta fourth order fixed step numerical method [_{is }- 1/_{is }respectively. The differential equation system solutions were used to calculate daily incidence, taking into account parameters in Table

_{sp}_{ids}

in which

For each scenario in Table

The asymptotic variance-covariance matrix of the least squares estimates of _{0}, _{E }and _{I}, with associated standard deviations and confidence intervals.

As morbidity and mortality data are not linked at the individual level, case-fatality lag was modelled by using convolution. A least-squares gamma distribution was fitted to the observed incidence curve. A gamma distribution with the same scale parameter was then fitted to mortality data. Utilising these distributions and the convolution formula, a gamma distributed incidence-mortality lag distribution, with the same scale parameter, was obtained.

Gamma distributions with the same scale parameter were then fitted to the best-fit deterministic models of daily incidence. These distributions, convolved with the incidence-mortality lag distribution, yielded daily mortality distributions for each of Scenarios 1 to 3. A common scale parameter was used in the above convolutions in order to obtain closed-form (gamma) probability density functions.

Best-fit incidence curves from the SEIR model for the three scenarios are shown in Figure _{0}, _{E }and _{I }values, are shown in Table _{0 }values ranged between 1.3, and 3.1, and corresponding average latent period and infectious period estimates ranged between 0.7 and 1.3 days, and 0.2 and 0.3 days, respectively.

Observed and best-fit modelled incidence (ill cases per day) for Scenarios 1 to 3, and best-fit gamma distribution.

Rate constants and epidemiological parameters corresponding to the best-fit models shown in Figure 1 (associated standard deviation or 95% confidence interval is given in brackets).

^{-1}) | ^{-1}) | ^{-1}) | _{0} | _{E } | _{I }(days) | |

1 | 5.3 (0.50) | 1.5 (0.08) | 4.2 (0.33) | 1.3 (0.02) | 0.67 (0.60, 0.74) | 0.24 (0.21, 0.28) |

2 | 6.5 (0.27) | 1.2 (0.04) | 3.6 (0.11) | 1.8 (0.04) | 0.83 (0.78, 0.89) | 0.28 (0.26, 0.30) |

3 | 10.1 (1.55) | 0.8 (0.11) | 3.3 (0.36) | 3.1 (0.18) | 1.25 (0.99, 1.69) | 0.30 (0.25, 0.38) |

The gamma distribution of incidence-mortality lag time obtained by convolution is shown in Figure

Incidence-mortality lag time distribution.

Observed mortality data, shown in Figure

Observed and best-fit modelled mortality (deaths per day) for Scenarios 1 to 3.

This analysis has demonstrated the potential for using historical disease epidemic data to derive plausible, and potentially useful, pandemic influenza parameter estimates. This is the first time that these parameters have been reported for the 1918 pandemic outside of Europe, the USA and Brazil.

This work is limited by the very nature of using data from an event that occurred over eight decades ago. For example, the estimate of the camp's population was only approximate (at 8000). The mortality burden of this particular outbreak (at 20.4 per 1000) was also somewhat higher than that for the general male population of New Zealand (ie, at 10.0 per 1000 for 20–24 year olds) [

In addition to data limitations, the parameters used for the SEIR model also involve uncertainties; for example, we have no good data on the proportion of the young male population who were likely to be susceptible to this strain in 1918 (e.g. based on the possible residual immunity from the first wave of the pandemic or from previous influenza epidemics and pandemics). Also, the SEIR model involves a number of simplifying assumptions, including a single index case, homogeneous mixing, exponentially distributed residence times in infectious status categories, and isolation of the military camp.

The estimates for _{0 }in the range from 1.3 to 3.1 are the first such estimates for the 1918 pandemic outside Europe, the United States and Brazil, so far as we are aware. However, given the unique aspects of the military camp (crowded conditions and a young population with low immunity) it is quite likely that the _{0 }values estimated in our analysis might tend to over-estimate those for the general population. Nevertheless, this effect may have been partly offset by the camp policy of immediate hospitalisation upon symptoms, effectively reducing infective contacts.

Our estimated range for _{0 }is broadly consistent with estimates for this pandemic in the United States (a median _{0 }of 2.9 for 45 cities) [_{0 }= 3.1) may reflect the differences between disease transmission in the general population (as per the above cited studies) and transmission in a crowded military camp with a predominance of young males.

Considered collectively, these _{0 }estimates for pandemic influenza in various countries are not particularly high when compared to the _{0 }estimates for various other infectious diseases [_{0 }values in the 1.1 to 2.4 range, has suggested the possibility of successful influenza pandemic control [_{0 }= 1.8 [_{0}, control measures may be more difficult, especially if public health authorities are slow to respond and they have insufficient access to antivirals and pandemic strain vaccines.

The average latent and infectious periods were estimated to be in the range between 0.7 to 1.3 days, and 0.2 to 0.3 days, respectively. The infectious period is short compared to the period of peak virus shedding known to occur in the first 1 to 3 days of illness [

The fast onset and subsequent decline of the outbreak in the Featherston Military Camp, as compared to a national or city-wide outbreak, might possibly be due to relatively close habitation and a high level of mixing. The average time for infection between a primary and secondary case (the serial interval) is greatly shortened in this case. This could explain a short apparent infectious period, and a relatively large proportion of the serial interval in the latent state. Another possible explanation of the relatively short apparent infectious period for this outbreak is that it may reflect the limited transmission that occurred once symptomatic individuals were hospitalised on diagnosis – which was the policy taken in this military camp for all cases.

This analysis was able to estimate an approximate seven-day delay from reported symptomatic illness to the date of death at a population level. This result is suggestive that even in this relatively young population (largely of military recruits), an important cause of death was likely to have been from secondary bacterial pneumonia – as opposed to the primary influenza viral pneumonia or acute respiratory distress syndrome (for which death may have tended to occur more promptly). This finding is consistent with other evidence that a large proportion of deaths from the 1918 pandemic was attributable to bacterial respiratory infections [

The _{0 }estimates in the 1.3 to 3.1 range are broadly consistent with others made for the 1918 influenza pandemic and are not particularly large relative to some other infectious diseases. This finding suggests that if a novel influenza strain of similar virulence emerged then it could potentially be controlled through the prompt use of major public health measures. These results also suggest that effective treatment of pneumonia could result in better outcomes (lower mortality) than was experienced in 1918.

The author(s) declare that they have no competing interests.

Three of authors were involved in initial work in identifying the data and analysing it from a historical and epidemiological perspective (PN, NW and MB). The other two authors worked on developing and running the mathematical model (GS, MR). GS did most of the drafting of the first draft of the manuscript with assistance from NW. All authors then contributed to further re-drafting of the manuscript and have given approval of the final version to be published.

We thank the following medical students for their work in gathering information on the outbreak in the Featherston military camp: Abdul Al Haidari, Abdullah Al Hazmi, Hassan Al Marzouq, Melinda Parnell, Diana Rangihuna, Yasotha Selvarajah. We also thank the journal's reviewers for their helpful comments. Some of the work on this article by two of the authors (NW & MB) was part of preparation for a Centers for Disease Control and Prevention (USA) grant (1 U01 CI000445-01).